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Question

A circle S passes through the point (0,1) and is orthogonal to the circles (x1)2+y2=16 and x2+y2=1, then

A
radius of S is 8
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B
radius of S is 7
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C
centre of S is (7,1)
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D
centre of S is (8,1)
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Solution

The correct option is C centre of S is (7,1)
Let the circle be,
x2+y2+2gx+2fy+c=0
Condition for orthogonality,
2g1g2+2f1f2=c1+c2
Orthogonal with
(x1)2+y2=16x2+y22x15=0
Applying condition for orthogonality,
2g(1)+0=c15(1)

Orthogonal with
x2+y21=0
Applying condition for orthogonality,
0+0=c1c=1(2)
From using equation (1),
g=7
Putting the point (0,1) in the circle,
1+2f+1=0f=1
Therefore the equation of the circle will be,
x2+y2+14x2y+1=0(x+7)2+(y1)2=49
Centre =(7,1)
radius =7


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